Rigorous parameter reconstruction for differential equations with noisy data

• We present a method that–given a data set, a finitely parametrized system of ordinary differential equations (ODEs), and a search space of parameters–discards portions of the search space that are inconsistent with the model ODE and data. The method is completely rigorous as it is based on validated integration of the vector field. As a consequence, no consistent parameters can be lost during the pruning phase. For data sets with moderate levels of noise, this yields a good reconstruction of the underlying parameters. Several examples are included to illustrate the merits of the method.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Primary: 65G20

34A60

Secondary: 65L09

rigorous numerics

parameter estimation

ordinary differential equations

interval analysis

MATHEMATICS

MATEMATIK

matematik

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)